Topological spin Hall states, charged skyrmions, and superconductivity in two dimensions

TL;DR

This paper explores two-dimensional topological spin Hall insulators with spontaneous spin symmetry breaking, revealing that skyrmions carry electric charge and that their condensation can lead to superconductivity, including a possible second-order phase transition.

Contribution

It demonstrates that skyrmions in these insulators carry twice the electron charge and shows how their condensation induces superconductivity, highlighting a novel phase transition.

Findings

Skyrmions in the phase carry double electron charge.

Condensation of skyrmions leads to superconductivity.

The superconductor-spin Hall insulator transition can be second order.

Abstract

We study the properties of two dimensional topological spin hall insulators which arise through spontaneous breakdown of spin symmetry in systems that are spin rotation invariant. Such a phase breaks spin rotation but not time reversal symmetry and has a vector order parameter. Skyrmion configurations in this vector order parameter are shown to have electric charge that is twice the electron charge. When the spin Hall order is destroyed by condensation of skyrmions superconductivity results. This may happen either through doping or at fixed filling by tuning interactions to close the skyrmion gap. In the latter case the superconductor- spin Hall insulator quantum phase transition can be second order even though the two phases break distinct symmetries.